Improvement of Controlled Bidirectional Quantum Direct Communication Using a GHZ State

The security of controlled bidirectional quantum direct communication using a GHZ state [Chin. Phys. Lett. 23 (2006) 1680] is analyzed. It turns out that the MX protocol has the problem of definite information leakage, i.e., the first bit of a secret message from any communication party is always leaked out without any active attack after the controller's announcement of measurement results. We put forward two approaches to improve this. The first is to merely modify the encoding rule of the MX protocol, while the second is to use a Bell state as the quantum resource instead of a GHZ state. Both our approaches can ensure that all the bits of secret messages from two communication parties are not leaked out after the controller's announcement of measurement results. Moreover, the controlled bidirectional quantum secure direct communication protocol based on the second approach is more convenient to implement than the MX protocol, since it merely uses a Bell state as the quantum resource and only needs to perform the Bell-basis measurement.